Question

please answer q 10 &11​

Answer 1

Step-by-step explanation:

10. if x-1/x=3+2√2

${x}^{3} - \frac{1}{ {x}^{3}} =(x - \frac{1}{x})( {x}^{2} + \frac{1}{{x}^{2} } + 1) =$

$(3 + 2 \sqrt{2})( {(x - \frac{1}{x})}^{2} + 2 + 1) =$

$= (3 + 2 \sqrt{2})( {(3 + 2 \sqrt{2)}}^{2} + 3) =$

$= (3 + 2 \sqrt{2)} (9 + 8 + 12 \sqrt{2} + 3) =$

$= (3 + 2 \sqrt{2})(20 + 12 \sqrt{2}) =$

$=60 + 36 \sqrt{2} + 40 \sqrt{2} + 48 = 108 +$

$76 \sqrt{2}$

11. x+1/x = 3 1/3= 10/3

Square on both sides , we get

${(x + \frac{1}{x})}^{2} = \frac{100}{9} = > {x}^{2} + \frac{1}{ {x}^{2}} + 2 =$

$\frac{100}{9} = >$

Subtract 4 on both sides we get

$= > {x}^{2} + \frac{1}{ {x}^{2}} - 2 = \frac{100}{9} - 4 = \frac{100 - 36}{9}$

$= > {(x - \frac{1}{x}) }^{2} = \frac{64}{9} = > x - \frac{1}{x} = \sqrt{ \frac{64}{9} }$

$= > x - \frac{1}{x} = \frac{8}{3}$

So

${x}^{3} - \frac{1}{ {x}^{3} } = (x - \frac{1}{x})( {x}^{2} + \frac{1}{ {x}^{2} } + 1) =$

$\frac{8}{3}( {(x - \frac{1}{x}) }^{2} + 2 + 1) = \frac{8}{3}( { \frac{8}{3} }^{2} + 3) =$

$= \frac{8}{3}( \frac{64}{9} + 3) = \frac{8}{3} ( \frac{64 + 27}{9}) = \frac{728}{27} =$

$26 \frac{26}{27}$

Hope it helps you.